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Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games

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  • Hamadène, Said
  • Mu, Rui

Abstract

In this paper, we study a nonzero-sum stochastic differential game in the Markovian framework. We show the existence of a discontinuous Nash equilibrium point for this game. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component.

Suggested Citation

  • Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6901-6926
    DOI: 10.1016/j.spa.2020.07.003
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    References listed on IDEAS

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    1. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    2. Pierre Cardaliaguet & Slawomir Plaskacz, 2003. "Existence and uniqueness of a Nash equilibrium feedback for a simple nonzero-sum differential game," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 33-71, December.
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    4. A. Bensoussan & J. Frehse, 2000. "Stochastic Games for N Players," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 543-565, June.
    5. Paola Mannucci, 2014. "Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians," Dynamic Games and Applications, Springer, vol. 4(3), pages 329-344, September.
    6. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    7. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    8. Lin, Qian, 2015. "Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4405-4454.
    9. Fan, ShengJun & Jiang, Long, 2012. "One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1792-1798.
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    Cited by:

    1. Hu, Zuopeng & Yang, Yanlong, 2024. "Existence and generic stability of open-loop Nash equilibria for noncooperative fuzzy differential games," Applied Mathematics and Computation, Elsevier, vol. 463(C).

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